Question

The average helicopter is \[12.5{\text{ }}m{\text{ }}long\]. If a Tyrannosaurus is thought to have been about \[15.2{\text{ }}m{\text{ }}long\]. What is the absolute value of difference between the lengths of a helicopter and a Tyrannosaurus.

Answer 1

Hint: Absolute value of difference is always positive.
First, we are going to write down the given values, then after we subtract them and then after subtracting, we get the difference, since we are finding absolute difference, we have applied modulus to the subtraction operation, such that absolute value of the difference is obtained. \[\left| {x{\text{ }} - {\text{ }}y} \right|{\text{ }} \geqslant {\text{ }}0\], since absolute value is always non-negative.

Complete step-by-step answer:
First, we are given that
Helicopter is \[12.5{\text{ }}m{\text{ }}long\] and tyrannosaurus is \[15.2{\text{ }}m{\text{ }}long\].
From this we have to find the absolute difference of the given above two.
So, the absolute difference of two real numbers x, y is given by \[\left| {x{\text{ }} - {\text{ }}y} \right|\].
Now, the absolute difference is
$
   = \left| {12.5 - {\text{ 15}}{\text{.2}}} \right| \\
   = \left| { - 2.7} \right| \\
   = 2.7 \;
$
Hence, we have found the absolute difference between the helicopter and the tyrannosaurus.
Since, we have applied the modulus function even if we do vice-versa of the difference, we will get the same answer.
Here are some of the properties of absolute difference.
 \[\left| {x{\text{ }} - {\text{ }}y} \right|{\text{ }} = {\text{ }}\left| {y{\text{ }} - {\text{ }}x} \right|\], since value is always non-negative.
 \[\left| {x{\text{ }} - {\text{ }}y} \right|{\text{ }} = {\text{ }}0\] if and only if \[x{\text{ }} = {\text{ }}y\].
 \[\left| {x{\text{ }} - {\text{ }}y} \right|{\text{ }} = {\text{ }}\left| {y{\text{ }} - {\text{ }}x} \right|\]
This follows since \[{\left| {x{\text{ }} - {\text{ }}y} \right|^{2{\text{ }}}} = {\text{ }}{\left( {x{\text{ }} - {\text{ }}y} \right)^2}\]and squaring is monotonic on the nonnegative reals.
So, the correct answer is “2.7”.

Note: We should always know that even if the difference comes out to be negative, it should be considered positive, as absolute difference is always non-negative and non-zero until \[x{\text{ }} = {\text{ }}y\]. There is no need for the largest number to be subtracted from in absolute difference.